Abstract: In actual production and sampling inspection, due to a variety of factors, the percentage of nonconforming products is often unknown and random, and inspection errors are also difficult to avoid. In order to reduce the risk and loss caused by sampling plans, the posterior risk probability of manufacturer and users is calculated by using the probability of inspection errors and the prior distribution of nonconforming product ratios in a batch. An integer nonlinear programming economic model based on imperfect inspection is established with a comprehensive consideration of sampling cost, reinspection cost and misjudgment loss. The optimal sampling plan is obtained and compared with the sampling plan without inspection errors. Finally, the effects of model parameters on the sampling plan and the two types of risks are discussed. Results show that the average total inspection with inspection errors is relatively large when defective rate of products is small; the average inspection quality of the two methods is very close, but the upper bound of the average outgoing quality with inspection errors is slightly lower than that without inspection errors.

Key words: imperfect inspection, sampling plan, economic model, defective rate